   Chapter 32, Problem 22PE

Chapter
Section
Textbook Problem

Naturally occurring 40K is listed as responsible for 16 mrem/y of background radiation. Calculate the mass of 40K that must be inside the 55−kg body of a woman to produce this dose. Each 40K decay emits a 1.32−MeV β, and 50% of the energy is absorbed inside the body.

To determine

The mass of 40K that must be inside a 55 kg body of a woman to produce a dose of 16 mrem/y of background radiation if 50% of the energy is absorbed by the body.

Explanation

Given info:

The background radiation dose

dose=16 mrem/y

Mass of the woman's body

m=55 kg

Energy of the emitted β particle

Eβ=1.32MeV

Half-life of 40K

t1/2=1.251×109y

Formula used:

The activity of a radioactive sample is given by,

R=0.693Nt1/2

Here, N is the number of atoms of the radioactive substance present.

The dose in rem is related to the dose in rad as follows:

dose in rem= dose in rad×RBE

Here RBE is the relative biological effectiveness.

Calculation:

dose in rad=dose in remRBE

The RBE for β particle is 1.

Therefore,

dose in rad=dose in remRBE=16 mrem/y1=16 mrad/y

Express the dose per year in J/kg.

The energy deposited in the woman for the radiation of the energy for a year as calculated above is given by,

E=radiation dose×mass of the woman

Therefore,

E=radiation dose×mass of the woman=1.60× 10 4J/kgy55 kg=8.80×103J/y

Express the energy in MeV/y.

E=8.80×103J/y×1 MeV1.6× 10 13J=5

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